Answer:
4. The equation of the perpendicular bisector is y = x -
5. The equation of the perpendicular bisector is y = - 2x + 16
6. The equation of the perpendicular bisector is y = x +
Step-by-step explanation:
Lets revise some important rules
- The product of the slopes of the perpendicular lines is -1, that means if the slope of one of them is m, then the slope of the other is
(reciprocal m and change its sign)
- The perpendicular bisector of a line means another line perpendicular to it and intersect it in its mid-point
- The formula of the slope of a line is
- The mid point of a segment whose end points are
and
is
- The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept
4.
∵ The line passes through (7 , 2) and (4 , 6)
- Use the formula of the slope to find its slope
∵ = 7 and
= 4
∵ = 2 and
= 6
∴
- Reciprocal it and change its sign to find the slope of the ⊥ line
∴ The slope of the perpendicular line =
- Use the rule of the mid-point to find the mid-point of the line
∴ The mid-point =
∴ The mid-point =
- Substitute the value of the slope in the form of the equation
∵ y = x + b
- To find b substitute x and y in the equation by the coordinates
of the mid-point
∵ 4 = ×
+ b
∴ 4 = + b
- Subtract from both sides
∴ = b
∴ y = x -
∴ The equation of the perpendicular bisector is y = x -
5.
∵ The line passes through (8 , 5) and (4 , 3)
- Use the formula of the slope to find its slope
∵ = 8 and
= 4
∵ = 5 and
= 3
∴
- Reciprocal it and change its sign to find the slope of the ⊥ line
∴ The slope of the perpendicular line = -2
- Use the rule of the mid-point to find the mid-point of the line
∴ The mid-point =
∴ The mid-point =
∴ The mid-point = (6 , 4)
- Substitute the value of the slope in the form of the equation
∵ y = - 2x + b
- To find b substitute x and y in the equation by the coordinates
of the mid-point
∵ 4 = -2 × 6 + b
∴ 4 = -12 + b
- Add 12 to both sides
∴ 16 = b
∴ y = - 2x + 16
∴ The equation of the perpendicular bisector is y = - 2x + 16
6.
∵ The line passes through (6 , 1) and (0 , -3)
- Use the formula of the slope to find its slope
∵ = 6 and
= 0
∵ = 1 and
= -3
∴
- Reciprocal it and change its sign to find the slope of the ⊥ line
∴ The slope of the perpendicular line =
- Use the rule of the mid-point to find the mid-point of the line
∴ The mid-point =
∴ The mid-point =
∴ The mid-point = (3 , -1)
- Substitute the value of the slope in the form of the equation
∵ y = x + b
- To find b substitute x and y in the equation by the coordinates
of the mid-point
∵ -1 = × 3 + b
∴ -1 = + b
- Add to both sides
∴ = b
∴ y = x +
∴ The equation of the perpendicular bisector is y = x +